---
title: "Challenges of Numbers Needed to Treat in HEOR"
output: 
  flexdashboard::flex_dashboard:
    storyboard: true
    theme: readable
    css: "style.css"
    social: menu
    source: embed
editor_options: 
  chunk_output_type: console
---

```{r setup, include=FALSE}
library(flexdashboard)
library(svglite)
library(dplyr)
devtools::load_all()
```


### How many will it take?

```{r ft.width = 10}

cols <- c(
  "#0094b6", # Light blue
  "#375180", # Dark blue
  "#ffce3f" # sunset
)

data.frame(p = c(30, 40),
           x = c("Placebo","Treatment")) %>%
  ggplot2::ggplot(ggplot2::aes(x = x, y = p, fill = x)) +
  ggplot2::geom_col() +
  ggplot2::scale_fill_manual(values = cols[2:3]) +
  ggplot2::coord_cartesian(ylim = c(0, 80)) +
  ggplot2::annotate(geom = "text", x = "Placebo", y = 50, label = "30%") +
  ggplot2::annotate(geom = "text", x = "Treatment", y = 50, label = "40%") +
  ggplot2::annotate(geom = "segment", x = "Placebo", xend = "Treatment", y = 60, yend = 60) +
  ggplot2::annotate(geom = "segment", x = "Placebo", xend = "Placebo",
                    y = 52, yend = 60) +
  ggplot2::annotate(geom = "segment", x = "Treatment", xend = "Treatment",
                    y = 52, yend = 60) +
  ggplot2::annotate(geom = "text", x = 1.5, y = 69, label = "Risk Difference (RD) = 0.1\nNNT = 1 / RD = 10\nWe have to treat 10 patients for one to benefit") +
  ggplot2::labs(title = stringr::str_wrap("Number Needed to Treat (NNT) provides a simple, clinically relevant summary of the observed effect in a given trial", 70),
                x = ggplot2::element_blank(),
                y = "Percent with event") +
  ggplot2::theme_minimal(base_size = 10) +
  ggplot2::theme(legend.position = "none")
  

```

------

The Number Needed to Treat is a concept promoted by some clinicians to help
understand the clinical significance of treatment effects. Since NNTs are
calculated based on absolute measures of effect, they can provide important
context since sometimes a small relative risk can be a big difference and a
large relative risk can be a small one


### Which effect is portable?


```{r, fig.width= 9,fig.height = 7, dev = "svglite"}

p <- seq(from = 0.05, to = 0.5, by = 0.05)

mod <- c("rr","or","rd")

est <- function(p, te, mod){
  if(mod == "rr") out <- p * te
  if(mod == "rd") out <- p + te
  if(mod == "or") out <- plogis(qlogis(p) + log(te))
  
  return(out)
} 

p_risks <- function(mod, te){
  tibble::tibble(
  p1 = p,
  p2 = est(p1, te, mod),
  rr = p2/p1,
  rd = p2 - p1,
  or = exp(qlogis(p2) - qlogis(p1))
) %>%
  tidyr::pivot_longer(names_to = "effect",
                      values_to = "estimate",
                      cols = -c(p1,p2)) %>%
  dplyr::mutate(mod = mod)

}


purrr::map2_df(c("rr","or","rd"), c(2, 5, 0.2), p_risks) %>%
  dplyr::filter(effect == "rd") %>%
  dplyr::mutate(p1 = round(p1*100,2)) %>%
  ggplot2::ggplot(ggplot2::aes(x = p1, y = estimate, color = mod)) +
  ggplot2::geom_smooth(se = FALSE) +
  ggplot2::theme_minimal(base_size = 16) +
  ggplot2::scale_color_manual(values= cols,
                              breaks = c("or", "rr", "rd")) +
  ggplot2::labs(
    title = "Risk difference varies depending on whether odds ratios, relative risks or risk differences are assumed to be constant across settings",
    x = "Baseline Risk (%)",
    y = "Risk Difference"
  ) +
  ggplot2::theme(
    plot.title = ggtext::element_textbox_simple(height = grid::unit(0.3, "npc")),
    legend.position = "none"
  ) +
  ggplot2::annotate(
    geom = "label", x = 10, y = 0.35, label = "Constant OR of 5",
    fill = cols[[1]], colour = "white"
  ) +
  ggplot2::annotate(
    geom = "label", x = 18, y = 0.25, label = "Constant RR of 2",
    fill = cols[[2]], colour = "white"
  ) +
  ggplot2::annotate(
    geom = "label", x = 30, y = 0.17, label = "Constant RD of 0.2",
    fill = cols[[3]], colour = "black"
  )
```

------------------------------------------------------------------------

When interpreting any given study and the comparisons within it, NNTs can
be a standalone summary of the observed effect. Since
trial populations might differ from practice in any given location we need to
make an assumption about the scale on which treatment effects are expected to
be portable. For binary outcomes common choices are the odds ratio, the
relative risk, or risk difference. It's not likely that any of these are strictly
true but one argument in favour of odds ratios is that they are the only of the
three that can have a constant effect across all possible baseline risk. 


### Implications for Meta-Analyses and Guidelines

```{r dev = "svglite", fig.width = 9}

or <- 1/3
p <- seq(from = 0.01, to = 0.25, by = 0.05)

rd_or <- plogis(qlogis(p) + log(or)) - p

tibble::tibble(
  p = glue::glue("{round(p*100,2)}%"),
  or,
  rd_or,
  nnt_or = abs(1/rd_or)
  ) %>%
  dplyr::mutate_at(dplyr::vars(-p),round,2) %>%
  flextable::flextable() %>%
  flextable::fontsize(size = 20, part = "all") %>%
  flextable::set_table_properties(layout = "autofit", width = 0.8) %>%
  flextable::set_header_labels(
    p = "Baseline\nRisk",
    or = "Odds\nRatio",
    rd_or = "Risk\nDifference",
    nnt_or = "Number Needed\nto Treat"
  ) %>%
  flextable::theme_zebra(
    odd_body = cols[[3]],
    odd_head = cols[[2]]
  ) %>%
  flextable::align(align = "center", part = "all") %>%
  flextable::color(color = "white", part = "header") %>%
  flextable::border_inner_v(border = officer::fp_border(color = cols[[2]], width = 2))
  

```

------------------------------------------------------------------------

It is tempting to summarize ITCs in terms of NNTs to help guide interpretations
about the clinical significance of differences between therapies. For example,
recommendations based on absolute outcomes/interpretation of their relevance is
incorporated in GRADE evidence summaries and used to help guideline panels. Unfortunately this can present issues when baseline risk varies across studies or
locations since the same treatment effect could make two comparators appear to
be virtually identical or drastically different in terms of NNTs.